Results 41 to 50 of about 60,664 (263)

A new class of travelling wave solutions for local fractional diffusion differential equations

Advances in Difference Equations, 2020
In this paper, we investigate a 3-D diffusion equation within the scope of the local fractional derivative. For this model, we establish local fractional vector operators and a local fractional Laplace operator defined on Cantor-type cylindrical ...
Ziyue Shi, Wei Qi, Jing Fan
doaj   +1 more source

Generative Fractional Diffusion Models

Advances in Neural Information Processing Systems 37
We introduce the first continuous-time score-based generative model that leverages fractional diffusion processes for its underlying dynamics. Although diffusion models have excelled at capturing data distributions, they still suffer from various limitations such as slow convergence, mode-collapse on imbalanced data, and lack of diversity. These issues
Nobis, Gabriel, Springenberg, Maximilian, Aversa, Marco, Detzel, Michael, Daems, Rembert, Murray-Smith, Roderick, Nakajima, Shinichi, Lapuschkin, Sebastian, Ermon, Stefano, Birdal, Tolga, Opper, Manfred, Knochenhauer, Christoph, Oala, Luis, Samek, Wojciech   +13 more
openaire   +4 more sources

Re‐Irradiation in Pediatric Diffuse Midline Glioma: A Multi‐Institutional Retrospective Study

Pediatric Blood &Cancer, EarlyView.
ABSTRACT Background Children with recurrent diffuse midline gliomas (DMGs) have limited therapeutic options at recurrence. Re‐irradiation (RT2) may be used at progression, but with uncertainty about the benefit. Methods We conducted a multi‐institutional retrospective study of children aged < 18 with DMG treated at three centers (Toronto, Canada ...
Ajay Thomas Alex, Sean P. Hassan, Helen Benghiat, Liam Herbert, Jennifer Adamski, Shivani Bailey, Claire Esler, Louise Brookes, Molly Bamber, Grace Koudou, Karen Waite, Julie Bennett, Anirban Das, Derek S. Tsang   +13 more
wiley   +1 more source

Numerical solution of fractional diffusion equation by Chebyshev collocation method and residual power series method

Alexandria Engineering Journal, 2020
In this paper, we propose an efficient Chebyshev collocation scheme to solve diffusion problem including time fractional diffusion equation considering the fractional derivative in the Liouville-Caputo sense. By making use of shifted Chebyshev polynomial
Mine Aylin Bayrak, Ali Demir, Ebru Ozbilge   +2 more
doaj   +1 more source

The planar cell polarity protein Vangl2 interacts with the PDZ‐domains of Scribble but not with a unique PDZ‐like domain in Inturned

FEBS Letters, EarlyView.
Structural and biochemical characterisations show that the planar cell polarity (PCP) protein Inturned harbours a unique PDZ‐like domain that does not bind canonical PDZ‐binding motifs (PBMs) like that of another PCP protein Vangl2. In contrast, the apical‐basal polarity protein Scribble contains four PDZ domains that bind Vangl2, but one PDZ domain ...
Stephan Wilmes, Jan Brysch, Carmen Gelze, Lilli Meier, Daniel Kümmel   +4 more
wiley   +1 more source

Fundamental solution of the model equation of anomalous diffusion of fractional order

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2015
Fundamental solution of the model equation of anomalous diffusion with Riemann-Liouville operator is constructed. Using the properties of the integral transformation with Wright function in kernel, we give estimates for the fundamental solution. When the
Fatima G Khushtova
doaj   +1 more source

Molecular Communication in Fractional Diffusive Channel [PDF]

IEEE Communications Letters, 2020
The molecular communication system with anomalous/fractional diffusion inside a one-dimensional (1-D) environment is considered. The time-dependent diffusivity is incorporated in terms of the power-law diffusivity, and the expression of first passage time density (FPTD) is derived.
Lokendra Chouhan, Prabhat Kumar Sharma, Adam Noel   +2 more
openaire   +1 more source

Valosin‐containing protein counteracts ATP‐driven dissolution of FUS condensates through its ATPase activity in vitro

FEBS Letters, EarlyView.
Biomolecular condensates formed by fused in sarcoma (FUS) are dissolved by high ATP concentrations yet persist in cells. Using a reconstituted system, we demonstrate that valosin‐containing protein (VCP), an AAA+ ATPase, counteracts ATP‐driven dissolution of FUS condensates through its D2 ATPase activity.
Hitomi Kimura, Shin‐ichi Tate, Kyota Yasuda   +2 more
wiley   +1 more source

Distinctive Shape Functions of Fractional Differential Quadrature for Solving Two-Dimensional Space Fractional Diffusion Problems

Fractal and Fractional, 2023
The aim of this study is to utilize a differential quadrature method with various kernels, such as Lagrange interpolation and discrete singular convolution, to tackle problems related to the Riesz fractional diffusion equation and the Riesz fractional ...
Abdelfattah Mustafa, Ola Ragb, Mohamed Salah, Reda S. Salama, Mokhtar Mohamed   +4 more
doaj   +1 more source

Sparse Optimal Control for Fractional Diffusion [PDF]

Computational Methods in Applied Mathematics, 2017
Abstract We consider an optimal control problem that entails the minimization of a nondifferentiable cost functional, fractional diffusion as state equation and constraints on the control variable. We provide existence, uniqueness and regularity results together with first-order optimality conditions.
Enrique Otárola, Abner J. Salgado
openaire   +3 more sources